Related papers: Quantum Expectation-Maximization Algorithm
Quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size.…
We study the convergence behavior of the Expectation Maximization (EM) algorithm on Gaussian mixture models with an arbitrary number of mixture components and mixing weights. We show that as long as the means of the components are separated…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
The Incremental K-means (IKM), an improved version of K-means (KM), was introduced to improve the clustering quality of KM significantly. However, the speed of IKM is slower than KM. My thesis proposes two algorithms to speed up IKM while…
In this paper, we outline the use of Mixture Models in density estimation of large astronomical databases. This method of density estimation has been known in Statistics for some time but has not been implemented because of the large…
Clustering is an essential task to unsupervised learning. It tries to automatically separate instances into coherent subsets. As one of the most well-known clustering algorithms, k-means assigns sample points at the boundary to a unique…
Vibration-based condition monitoring systems are receiving increasing attention due to their ability to accurately identify different conditions by capturing dynamic features over a broad frequency range. However, there is little research…
$k$-means clustering is a well-studied problem due to its wide applicability. Unfortunately, there exist strong theoretical limits on the performance of any algorithm for the $k$-means problem on worst-case inputs. To overcome this barrier,…
We revisit the randomized seeding techniques for k-means clustering and k-GMM (Gaussian Mixture model fitting with Expectation-Maximization), formalizing their three key ingredients: the metric used for seed sampling, the number of…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our algorithm achieves high-performance by evaluating distances of datapoints with a subset of the cluster centres. Our…
The $k$-means algorithm is arguably the most popular nonparametric clustering method but cannot generally be applied to datasets with incomplete records. The usual practice then is to either impute missing values under an assumed…
In the modal approach to clustering, clusters are defined as the local maxima of the underlying probability density function, where the latter can be estimated either non-parametrically or using finite mixture models. Thus, clusters are…
Nearest-neighbour clustering is a powerful set of heuristic algorithms that find natural application in the decoding of signals transmitted using the M-Quadrature Amplitude Modulation (M-QAM) protocol. Lloyd et al. proposed a quantum…
Expectation Maximization (EM) is the standard method to learn Gaussian mixtures. Yet its classic, centralized form is often infeasible, due to privacy concerns and computational and communication bottlenecks. Prior work dealt with data…
We derive an asymptotic expansion for the log likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for…
Clustering is a separation of data into groups of similar objects. Every group called cluster consists of objects that are similar to one another and dissimilar to objects of other groups. In this paper, the K-Means algorithm is implemented…
Many common clustering methods cannot be used for clustering multivariate longitudinal data in cases where variables exhibit high autocorrelations. In this article, a copula kernel mixture model (CKMM) is proposed for clustering data of…